Let’s Take a Break: Trends and Cycles in US Real GDP

Abstract:
Recent work on trend-cycle decompositions for US real GDP yields the following features: methods based on Unobserved Components models, the Beveridge-Nelson decomposition, the Hodrick-Prescott filter and others yield very different cycles which bear little resemblance to the NBER chronology, ascribes much movements to the trend leaving little to the cycle, and some imply a negative correlation between the noise to the cycle and the trend. We argue that these features are artifacts created by the neglect of a change in the slope of the trend function in real GDP in 1973. Once this is properly accounted for, all methods yield the same cycle with a trend that is non-stochastic except for a few periods around 1973. This cycle is more important in magnitude than previously reported, it accords well with the NBER chronology and implies no correlation between the trend and cycle, since the former is non-stochastic. Our results are corroborated using an alternative trend-cycle decomposition based on a generalized Unobserved Components models with errors having a mixture of Normals distribution for both the slope of the trend function and the cyclical component. It can account endogenously for infrequent changes such as level shifts and change in slope, as well as different variances for expansions and recessions. It yields a decomposition that accords very well with common notions of the business cycle.